Universität zu Köln

Bucchia, Beatrice and Heuser, Christoph (2015). Long-run variance estimation for spatial data under change-point alternatives. J. Stat. Plan. Infer., 165. S. 104 - 127. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 1873-1171

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Abstract

In this paper, we consider the problem of estimating the long-run variance (matrix) of an R-P-valued multiparameter stochastic process {X-K}(K epsilon[1,n]d), (n, p, d epsilon N, p, d fixed) whose mean-function has an abrupt jump. We consider processes of the form X-K = Y-K + mu + I-Cn(K)Delta, where I-C is the indicator function for a set C, the change-set C-n subset of [1, n](d) is a finite union of rectangles and mu, Delta epsilon R-P are unknown parameters. The stochastic process {Y-K : K epsilon Z(d)} is assumed to fulfill a weak invariance principle. Due to the non-constant mean, kernel-type long-run variance estimators using the arithmetic mean of the observations as a mean estimator have an unbounded error for changes Delta that do not vanish for n -> infinity. To reduce this effect, we use a mean estimator which is based on an estimation of the set C-n. In the case where C-n = ([n theta(0)(1)], [n theta(0)(2)]] is a rectangle, we introduce an estimator (C) over cap (n) = ([n (theta) over cap (1)], [n (theta) over cap (2)]] and study its convergence rate. (C) 2015 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bucchia, Beatrice UNSPECIFIED UNSPECIFIED UNSPECIFIED Heuser, Christoph UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-392569
DOI:	10.1016/j.jspi.2015.04.005
Journal or Publication Title:	J. Stat. Plan. Infer.
Volume:	165
Page Range:	S. 104 - 127
Date:	2015
Publisher:	ELSEVIER SCIENCE BV
Place of Publication:	AMSTERDAM
ISSN:	1873-1171
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RANDOM-FIELDS; CONVERGENCE; DEPENDENCE; SERIES; TESTS; POWER Multiple languages Statistics & Probability Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/39256